A flying wing design, previously developed as a senior project, was optimized for endurance using a gradient-based algorithm. Chord, sweep, taper ratio, and wingspan were varied within the model while all other design parameters were held constant from the original design. The model was produced from a combination of basic equations for flying wing aircraft and was validated using the previous designs experimental results. These equations are presented and the design space is explored. The optimal design produced an aircraft with a smaller wingspan, but higher aspect ratio. This design increased predicted flight endurance by 15.5% and experimental flight endurance by 13%. The optimized design was constrained by material yield strength of the airframe structure and the aircraft static margin.